The Spartak Moscow forward suffered a knock to his left leg in Monday's 4-0 win over South Korea.
Following an MRI scan, Waris was found to have suffered the tear, with the Ghana Football Association yet to confirm details of when he is expected to return.
Doctor Baba Adam stated they will give the 22-year-old every chance to prove his fitness before their June 15 deadline for replacing players.
"We did an MRI on the quadriceps and what we realized is that, there was a tear," he told the GFA website.
"We hope to get him on to the field again pretty soon. However, we are still monitoring him to the deadline when we will give our final statement on his state of affairs.
"The FIFA deadline is 15 (June), so we will monitor till that day and see how things turn up."
Ghana begin their World Cup campaign against the United States on June 16 in Natal.
